light frequencies. Further developments Many recent experiments have focused on the application of the model to systems with potential applications in quantum information processing and coherent control. Various experiments have demonstrated the dynamics of the Jaynes–Cummings model in the coupling of a quantum dot to the modes of a micro-cavity, potentially allowing it to be applied in a physical system of much smaller size. Other experiments have focused on demonstrating the non-linear nature of the Jaynes-Cummings ladder of energy levels by direct spectroscopic observation. These experiments have found direct evidence for the non-linear behavior predicted from the quantum nature of the field in both superconducting circuits containing an "artificial atom" coupled to a very high quality oscillator in the form of a superconducting RLC circuit, and in a collection of Rydberg atoms coupled via their spins. In the latter case, the presence or absence of a collective Rydberg excitation in the ensemble serves the role of the two level system, while the role of the bosonic field mode is played by the total number of spin flips that take place. Theoretical work has extended the original model to include the effects of dissipation and damping, typically via a phenomenological approach. Proposed extensions have also incorporated the inclusion of multiple modes of the quantum field, allowing for coupling to additional energy levels within the atom, or the presence of multiple atoms interacting with the same field. Some attempt has also been made to go beyond the so-called rotating-wave approximation that is usually employed (see the mathematical derivation below). The coupling of a single quantum field mode with multiple () two-state subsystems (equivalent to spins higher than 1/2) is known as the Dicke model or the Tavis–Cummings model. For example, it applies to a high quality resonant cavity containing multiple identical atoms with transitions near the cavity resonance, or a resonator coupled to multiple quantum dots on a superconducting circuit. It reduces to the Jaynes–Cummings model for the case . The model provides the possibility to realize several exotic theoretical possibilities in an experimental setting. For example, it was realized that during the periods of collapsed Rabi oscillations, the atom-cavity system exists in a quantum superposition state on a macroscopic scale. Such a state is sometimes referred to as a "Schrödinger cat", since it allows the exploration of the counter intuitive effects of how quantum entanglement manifests in macroscopic systems. It can